Development and application of methodology for the parametric analysis of complex survival and joint longitudinal-survival data in biomedical research

The occurrence of survival, or time-to-event, data is commonplace in medical research, where interest lies in the time it takes from a given baseline, for an event of interest to occur, and the factors that are associated with it. For example, this could be the effect of a treatment on the time to death since diagnosis of cardiovascular disease. The primary aim of this thesis is to develop parametric methods for the analysis of complex survival data, including the extension to joint models of longitudinal and survival data, to provide a number of advantages over the commonly used semi-parametric Cox model. New and current methodology is often assessed using simulation studies; however, often in the field of survival analysis they are simplistic and fail to reflect biologically plausible scenarios. In this thesis a general algorithm for simulating complex survival data, from any given hazard function, is proposed and assessed. A general framework for the parametric analysis of survival data is then developed, utilising numerical quadrature, illustrated in detail using the special case of restricted cubic splines to model the baseline hazard and time-dependent effects. Extensions to the framework including cluster robust standard errors and excess mortality models are also considered. Finally, the joint longitudinal-survival modelling framework is extended to incorporate the Royston- Parmar survival model, and a mixture of two parametric distributions, both evaluated through simulation, utilising the proposed simulation algorithm, showing advantages over more simple parametric approaches. The estimation of joint models, using Gaussian quadrature, is also evaluated through an extensive simulation study. Throughout the thesis, user friendly software is developed to implement the methodological components, allowing statisticians and non-statisticians alike, to apply the methods directly. A variety of clinical datasets in the areas of cancer, cardiovascular disease and liver cirrhosis are used to exemplify the proposals.